2x^2+60x-2700=0

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Solution for 2x^2+60x-2700=0 equation: 


Simplifying
2x2 + 60x + -2700 = 0

Reorder the terms:
-2700 + 60x + 2x2 = 0

Solving
-2700 + 60x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1350 + 30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1350 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-1350 + 30x + x2 = 0

Solving
-1350 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1350' to each side of the equation.
-1350 + 30x + 1350 + x2 = 0 + 1350

Reorder the terms:
-1350 + 1350 + 30x + x2 = 0 + 1350

Combine like terms: -1350 + 1350 = 0
0 + 30x + x2 = 0 + 1350
30x + x2 = 0 + 1350

Combine like terms: 0 + 1350 = 1350
30x + x2 = 1350

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 1350 + 225

Reorder the terms:
225 + 30x + x2 = 1350 + 225

Combine like terms: 1350 + 225 = 1575
225 + 30x + x2 = 1575

Factor a perfect square on the left side:
(x + 15)(x + 15) = 1575

Calculate the square root of the right side: 39.686269666

Break this problem into two subproblems by setting 
(x + 15) equal to 39.686269666 and -39.686269666.


Subproblem 1
x + 15 = 39.686269666

Simplifying
x + 15 = 39.686269666

Reorder the terms:
15 + x = 39.686269666

Solving
15 + x = 39.686269666

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + x = 39.686269666 + -15

Combine like terms: 15 + -15 = 0
0 + x = 39.686269666 + -15
x = 39.686269666 + -15

Combine like terms: 39.686269666 + -15 = 24.686269666
x = 24.686269666

Simplifying
x = 24.686269666


Subproblem 2
x + 15 = -39.686269666

Simplifying
x + 15 = -39.686269666

Reorder the terms:
15 + x = -39.686269666

Solving
15 + x = -39.686269666

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + x = -39.686269666 + -15

Combine like terms: 15 + -15 = 0
0 + x = -39.686269666 + -15
x = -39.686269666 + -15

Combine like terms: -39.686269666 + -15 = -54.686269666
x = -54.686269666

Simplifying
x = -54.686269666


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.686269666, -54.686269666}
Solution
x = {24.686269666, -54.686269666}

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